Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 4: Statistical physics in biological systems II (joint session DY/BP)

DY 4.6: Vortrag

Montag, 23. März 2009, 15:45–16:00, HÜL 386

Effects of intrinsic noise on models of epidemics — •Andrew Black and Alan McKane — School of Physics and Astronomy, The University of Manchester, UK

Demographic stochasticity, i.e. intrinsic noise introduced by the random interaction of agents in indivdual-based systems, can affect their macroscopic dynamics considerably. Models which in their deterministic mean-field limit approach a fixed point, can exhibit persistent macroscopic oscillations sustained by fluctuations on the microscopic level. In the work presented here we study the effects of demographic stochasticity and external forcing on individual-based models of epidemics. We show that the fluctuations present in the unforced versions of these stochastic models can be understood in terms of noise resonating with the systems natural frequency. Analytical progress can be made by formulating the system in terms of a master equation, from which the exact power spectrum of the fluctuations is derived using a van-Kampen expansion in the inverse system size. We show that even at large amplitude of the external forcing the magnitude and frequency of the stochastic oscillations can still be determined from the unforced model.